Iraq's prime minister, Nouri al-Maliki, and his predecessor, Ayad Allawi, are almost neck and neck in early counts after Sunday's general election, so far claiming two of the country's 18 provinces each.

Maliki was leading in the Shia conservative heartlands of Najaf and Babil, while Allawi appeared to have won the Sunni strongholds of Diyyala and Salahedin, according to the Independent High Election Commission (IHEC) .

Meanwhile, the first allegations of vote-rigging emerged in Baghdad.

Allawi's Iraqiya list claimed 55 of its candidates had been disqualified on the eve of the election as part of a contentious de-Ba'athification process – a claim that has yet to be verified.

Allawi would not put his name to the allegations, which offered scant detail and fell significantly short of a statement, released in the name of the Iraqiya list, that alleged "massive and unprecedented fraud".

"We found Iraqiya votes in rubbish bins," Adnan al-Janabi, a candidate, said. "Their votes thrown out of ballot boxes and neglected by the IHEC – and this is fraud."

Janabi and other Iraqiya candidates said they had received advice about irregularities today from the UN assistance mission in Iraq. UNAMI could not be reached for comment.

An IHEC board member, Qassem al-Abodi, said no allegations of irregularities had been raised with the commission.

"[Iraqiya] have not submitted any complaint," he said. "We don't rely on what is said in the media, only on legal procedures."

A credible ballot is considered to be crucial to a planned US withdrawal. It follows elections in Iran and Afghanistan, where results are widely considered to have been illegitimate.

Partial counting results from Iraq's 14 other provinces are expected to be released on Sunday.